2020-11-16 Matrices and Eigenvectors

380 days ago by calkin

B=matrix(3,3,[9,1,4,4,6,5,6,4,2]) 
       
show(B) 
       
v=vector([1,1,1.]) for i in srange(40): v=B*v v=v*1/sqrt(v.dot_product(v)) print i,v 
       
0 (0.588984426676340, 0.631054742867507, 0.504843794294005)
1 (0.579468416374704, 0.631589914143858, 0.515083036777515)
2 (0.577637252491366, 0.634303489358492, 0.513803744558044)
3 (0.576706722025234, 0.634984902089625, 0.514007325715440)
4 (0.576386952583560, 0.635287975134192, 0.513991507265767)
5 (0.576261756393118, 0.635396324189626, 0.513997956537797)
6 (0.576215003744096, 0.635438109111163, 0.513998714929738)
7 (0.576197250254645, 0.635453793601029, 0.513999226650242)
8 (0.576190548755976, 0.635459738242235, 0.513999389685821)
9 (0.576188013733646, 0.635461983662914, 0.513999455397445)
10 (0.576187055516810, 0.635462832849979, 0.513999479689570)
11 (0.576186693221585, 0.635463153861997, 0.513999488947351)
12 (0.576186556253341, 0.635463275230748, 0.513999492437421)
13 (0.576186504469773, 0.635463321115532, 0.513999493758235)
14 (0.576186484892203, 0.635463338463121, 0.513999494257409)
15 (0.576186477490571, 0.635463345021650, 0.513999494446155)
16 (0.576186474692263, 0.635463347501212, 0.513999494517510)
17 (0.576186473634316, 0.635463348438651, 0.513999494544487)
18 (0.576186473234342, 0.635463348793066, 0.513999494554686)
19 (0.576186473083125, 0.635463348927058, 0.513999494558542)
20 (0.576186473025955, 0.635463348977716, 0.513999494560000)
21 (0.576186473004341, 0.635463348996868, 0.513999494560551)
22 (0.576186472996170, 0.635463349004109, 0.513999494560760)
23 (0.576186472993080, 0.635463349006846, 0.513999494560838)
24 (0.576186472991912, 0.635463349007881, 0.513999494560868)
25 (0.576186472991471, 0.635463349008273, 0.513999494560879)
26 (0.576186472991304, 0.635463349008420, 0.513999494560884)
27 (0.576186472991241, 0.635463349008476, 0.513999494560885)
28 (0.576186472991217, 0.635463349008497, 0.513999494560886)
29 (0.576186472991208, 0.635463349008506, 0.513999494560886)
30 (0.576186472991204, 0.635463349008509, 0.513999494560886)
31 (0.576186472991203, 0.635463349008510, 0.513999494560886)
32 (0.576186472991203, 0.635463349008510, 0.513999494560886)
33 (0.576186472991203, 0.635463349008510, 0.513999494560886)
34 (0.576186472991202, 0.635463349008510, 0.513999494560886)
35 (0.576186472991202, 0.635463349008510, 0.513999494560886)
36 (0.576186472991202, 0.635463349008510, 0.513999494560886)
37 (0.576186472991202, 0.635463349008510, 0.513999494560886)
38 (0.576186472991202, 0.635463349008510, 0.513999494560886)
39 (0.576186472991202, 0.635463349008510, 0.513999494560886)
0 (0.588984426676340, 0.631054742867507, 0.504843794294005)
1 (0.579468416374704, 0.631589914143858, 0.515083036777515)
2 (0.577637252491366, 0.634303489358492, 0.513803744558044)
3 (0.576706722025234, 0.634984902089625, 0.514007325715440)
4 (0.576386952583560, 0.635287975134192, 0.513991507265767)
5 (0.576261756393118, 0.635396324189626, 0.513997956537797)
6 (0.576215003744096, 0.635438109111163, 0.513998714929738)
7 (0.576197250254645, 0.635453793601029, 0.513999226650242)
8 (0.576190548755976, 0.635459738242235, 0.513999389685821)
9 (0.576188013733646, 0.635461983662914, 0.513999455397445)
10 (0.576187055516810, 0.635462832849979, 0.513999479689570)
11 (0.576186693221585, 0.635463153861997, 0.513999488947351)
12 (0.576186556253341, 0.635463275230748, 0.513999492437421)
13 (0.576186504469773, 0.635463321115532, 0.513999493758235)
14 (0.576186484892203, 0.635463338463121, 0.513999494257409)
15 (0.576186477490571, 0.635463345021650, 0.513999494446155)
16 (0.576186474692263, 0.635463347501212, 0.513999494517510)
17 (0.576186473634316, 0.635463348438651, 0.513999494544487)
18 (0.576186473234342, 0.635463348793066, 0.513999494554686)
19 (0.576186473083125, 0.635463348927058, 0.513999494558542)
20 (0.576186473025955, 0.635463348977716, 0.513999494560000)
21 (0.576186473004341, 0.635463348996868, 0.513999494560551)
22 (0.576186472996170, 0.635463349004109, 0.513999494560760)
23 (0.576186472993080, 0.635463349006846, 0.513999494560838)
24 (0.576186472991912, 0.635463349007881, 0.513999494560868)
25 (0.576186472991471, 0.635463349008273, 0.513999494560879)
26 (0.576186472991304, 0.635463349008420, 0.513999494560884)
27 (0.576186472991241, 0.635463349008476, 0.513999494560885)
28 (0.576186472991217, 0.635463349008497, 0.513999494560886)
29 (0.576186472991208, 0.635463349008506, 0.513999494560886)
30 (0.576186472991204, 0.635463349008509, 0.513999494560886)
31 (0.576186472991203, 0.635463349008510, 0.513999494560886)
32 (0.576186472991203, 0.635463349008510, 0.513999494560886)
33 (0.576186472991203, 0.635463349008510, 0.513999494560886)
34 (0.576186472991202, 0.635463349008510, 0.513999494560886)
35 (0.576186472991202, 0.635463349008510, 0.513999494560886)
36 (0.576186472991202, 0.635463349008510, 0.513999494560886)
37 (0.576186472991202, 0.635463349008510, 0.513999494560886)
38 (0.576186472991202, 0.635463349008510, 0.513999494560886)
39 (0.576186472991202, 0.635463349008510, 0.513999494560886)